Factoris the expression.
`l ^(2) m ^(2) n - lm ^(2) n ^(2) - l^(2) mn ^(2)`

Write the greatest common factor in each of the term. l ^(2) m ^(2) n, l m ^(2) n ^(2) , l ^(2) mn ^(2)

If the each of algebraic expressions lx^(2) + mx + n, mx^(2) + nx + l and nx^(2) + lx + m are prefect squares, then (l +m)/(n) = _____

Factories: m^(4) + 2m^(2) n ^(2) +n ^(4)

|[(m+n)^(2), l^(2), mn], [(n+l)^(2), m^(2), ln], [(l+m)^(2), n^(2), lm]| =(l^(2) +m^(2) +n^(2))(l-m)(m-n)(n-l)(l+m+n)

Find the angle between the lines whose direction-cosines are given by : (i) l + m + n = 0, l^(2) + m^(2) - n^(2) = 0 (ii) 2l - m + 2n = 0 , mn + nl + lm = 0 ,

The roots of the equation l^(2)(m^(2)-n^(2))x^(2)+m^(2)(n^(2)-l^(2))x+n^(2)(I^(2)-m^(2))=0 are

8l^(3)-36l^(2)m+54lm^(2)-27m^(3)

Show that the matris [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] is orthogonal, if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).

If a^m .a^n = a^(mn) , then m(n - 2) + n(m- 2) is :